Author: Efstathios Vassiliou
Publisher: Springer Science & Business Media
ISBN: 1402034164
Category : Mathematics
Languages : en
Pages : 454
Book Description
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
Geometry of Principal Sheaves
Author: Efstathios Vassiliou
Publisher: Springer Science & Business Media
ISBN: 1402034164
Category : Mathematics
Languages : en
Pages : 454
Book Description
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
Publisher: Springer Science & Business Media
ISBN: 1402034164
Category : Mathematics
Languages : en
Pages : 454
Book Description
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
The Geometry of Moduli Spaces of Sheaves
Author: Daniel Huybrechts
Publisher: Cambridge University Press
ISBN: 1139485822
Category : Mathematics
Languages : en
Pages : 345
Book Description
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Publisher: Cambridge University Press
ISBN: 1139485822
Category : Mathematics
Languages : en
Pages : 345
Book Description
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Modern Differential Geometry in Gauge Theories
Author: Anastasios Mallios
Publisher: Springer Science & Business Media
ISBN: 0817646345
Category : Mathematics
Languages : en
Pages : 244
Book Description
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Publisher: Springer Science & Business Media
ISBN: 0817646345
Category : Mathematics
Languages : en
Pages : 244
Book Description
Original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
New Developments in Differential Geometry, Budapest 1996
Author: J. Szenthe
Publisher: Springer Science & Business Media
ISBN: 9401152764
Category : Mathematics
Languages : en
Pages : 513
Book Description
Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996
Publisher: Springer Science & Business Media
ISBN: 9401152764
Category : Mathematics
Languages : en
Pages : 513
Book Description
Proceedings of the Conference on Differential Geometry, Budapest, Hungary, July 27-30, 1996
Differential Sheaves And Connections: A Natural Approach To Physical Geometry
Author: Mallios Anastasios
Publisher: World Scientific
ISBN: 981471948X
Category : Mathematics
Languages : en
Pages : 304
Book Description
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
Publisher: World Scientific
ISBN: 981471948X
Category : Mathematics
Languages : en
Pages : 304
Book Description
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
100 Years of Chronogeometrodynamics: The Status of the Einstein’s Theory of Gravitation in Its Centennial Year
Author: Lorenzo Iorio
Publisher: MDPI
ISBN: 303842482X
Category : Electronic book
Languages : en
Pages : 469
Book Description
This book is a printed edition of the Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year" that was published in Universe
Publisher: MDPI
ISBN: 303842482X
Category : Electronic book
Languages : en
Pages : 469
Book Description
This book is a printed edition of the Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year" that was published in Universe
Algebraic Geometry
Author: Dan Abramovich
Publisher: American Mathematical Soc.
ISBN: 0821847023
Category : Mathematics
Languages : en
Pages : 506
Book Description
This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.
Publisher: American Mathematical Soc.
ISBN: 0821847023
Category : Mathematics
Languages : en
Pages : 506
Book Description
This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.
Geometry of Vector Sheaves
Author: Anastasios Mallios
Publisher: Springer Science & Business Media
ISBN: 9780792350057
Category : Mathematics
Languages : en
Pages : 468
Book Description
This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
Publisher: Springer Science & Business Media
ISBN: 9780792350057
Category : Mathematics
Languages : en
Pages : 468
Book Description
This is the second volume of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
Algebraic Cycles, Sheaves, Shtukas, and Moduli
Author: Piotr Pragacz
Publisher: Springer Science & Business Media
ISBN: 9783764385378
Category : Mathematics
Languages : en
Pages : 236
Book Description
Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Publisher: Springer Science & Business Media
ISBN: 9783764385378
Category : Mathematics
Languages : en
Pages : 236
Book Description
Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Connections on Principal Sheaves
Author: Efstathios Vassiliou
Publisher:
ISBN:
Category : Mechanics, Analytic
Languages : en
Pages : 36
Book Description
Publisher:
ISBN:
Category : Mechanics, Analytic
Languages : en
Pages : 36
Book Description